Question 1
Three similar-sized guavas together weigh 1 kg. About how much does each weigh?
Steps only
Share 1 kg equally among 3 guavas: 1÷3.
Answer
About 1/3 kg.
CLASS 6 · GANITA PRAKASH · CHAPTER 7
Fractions
Learn fractions through equal sharing, number lines, equivalent fractions, comparisons, addition and subtraction.
128 worked answersAll 9 end-of-chapter questions
What you will learn
- Interpret fractions as equal shares and fractional units.
- Locate, compare and convert fractions and mixed numbers.
- Add and subtract fractions by making their fractional units equal.
128 worked answers · short steps first, explanations when you need them
7.1 Fractions as Equal Shares
Textbook pages 151–153
Question 2
A merchant divides 1 kg of rice equally into four packets. What is the mass of each packet?
Steps only
1÷4=1/4 kg.
Answer
1/4 kg.
Question 3
Four friends share 3 glasses of juice equally. How much does each get?
Steps only
3 glasses÷4 friends=3/4 glass per friend.
Answer
3/4 glass each.
Question 4
A big fish weighs 1/2 kg and a small fish weighs 1/4 kg. What is their combined mass?
Steps only
Rewrite 1/2 as 2/4.
2/4+1/4=3/4.
Answer
3/4 kg.
Question 5
Put quarter, half, three quarters, one and a quarter, one and a half and two and a half in increasing order.
Steps only
In decimal form these are 0.25, 0.5, 0.75, 1.25, 1.5 and 2.5.
Answer
Quarter < half < three quarters < one and a quarter < one and a half < two and a half.
Question 6
How can you find the words people in your community use for fractions such as one and a half or three quarters?
Steps only
Ask family members, classmates or teachers for the words they use.
Write each word beside its fraction and note which languages use it.
Answer
Answers depend on the languages spoken around you. For example, the textbook notes Hindi “teen paav” and Tamil “mukkaal” for three quarters.
Question unit-fraction-size
Which is larger, 1/100 or 1/200? Explain using equal sharing.
Steps only
Imagine sharing one whole among 100 people, then among 200 people.
With twice as many equal shares, each share is smaller.
Answer
1/100 is larger than 1/200.
7.2 Fractional Units as Parts of a Whole
Textbook pages 154–155
Question 1
A whole chikki is cut into 6 equal parts in different shapes. Are the pieces the same size?
Steps only
Each piece is one of six equal shares of the same whole.
Answer
Yes, each is 1/6 of the chikki.
Question 2
What fraction of the whole is a piece made from 3 of 4 equal chikki parts?
Steps only
One part is 1/4; three parts are 3×1/4.
Answer
3/4 of the chikki.
Question 3(a)
What fraction of the whole is the first pictured piece?
Steps only
Count how many equal-sized copies of this piece would cover the whole.
Answer
1/12.
Question 3(b)
What fraction of the whole is the second pictured piece?
Steps only
Count the equal parts making the whole.
Answer
1/4.
Question 3(c)
What fraction of the whole is the third pictured piece?
Steps only
Count the equal parts making the whole.
Answer
1/3.
Question 3(d)
What fraction of the whole is the fourth pictured piece?
Steps only
Count the equal parts making the whole.
Answer
1/6.
Question 3(e)
What fraction of the whole is the fifth pictured piece?
Steps only
Count the equal parts making the whole.
Answer
1/8.
Question 3(f)
What fraction of the whole is the sixth pictured piece?
Steps only
Count the equal parts making the whole.
Answer
1/6.
Question 3(g)
What fraction of the whole is the seventh pictured piece?
Steps only
Count the equal parts making the whole.
Answer
1/24.
Question 3(h)
What fraction of the whole is the eighth pictured piece?
Steps only
Count the equal parts making the whole.
Answer
1/24.
7.3 Measuring Using Fractional Units
Textbook pages 156–158
Question 1
Continue the table for halves for two more steps after 5 halves.
Steps only
6×1/2=6/2=3.
7×1/2=7/2=3 1/2.
Answer
Six halves make 3 wholes; seven halves make 3 1/2 wholes.
Question 2
Write the first four repeated-addition statements for quarters.
Steps only
1/4; 1/4+1/4=2/4; add another 1/4 for 3/4; add one more for 4/4.
Answer
1/4; 2/4; 3/4; 4/4=1 whole.
Question 3
If a strip is folded into thirds, how can its length be used to make sixths?
Steps only
Halve each third.
Each half of 1/3 has length 1/6.
Answer
Fold each third in half to make six equal parts; each is 1/6.
Question 4(a)
Show 5 times 1/4 as an addition and fraction.
Steps only
Add five quarter units: 1/4+1/4+1/4+1/4+1/4.
That is 5/4=1 1/4.
Answer
5×1/4=5/4=1 1/4 roti.
Question 4(b)
Show 9 times 1/4 as an addition and fraction.
Steps only
Nine quarter-pieces make 9/4.
Group four quarters into each whole: 9/4=2 1/4.
Answer
9×1/4=9/4=2 1/4 rotis.
Question 5
How do you match 1/3, 1/5, 1/8 and 1/6 to pictures of one whole?
Steps only
For each picture, count how many equal pieces would cover the whole.
Match denominator 3, 5, 8 or 6 to that count.
Answer
Match each picture to the number of equal pieces that fill the whole: 1/3, 1/5, 1/8 or 1/6 respectively.
Question 6
Fill in the eighths table by adding one more 1/8 each time, from 2/8 through 8/8.
Steps only
3/8=1/8+1/8+1/8; continue counting eighths.
8/8 makes one whole.
Answer
2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 8/8=1.
7.4 Marking Fraction Lengths on the Number Line
Textbook pages 159–160
Question 1
A unit is divided into three equal parts. What fraction names the second mark?
Steps only
Each interval is 1/3.
The second mark is 2 intervals from zero.
Answer
2/3.
Question 2
A unit is divided into five equal parts. What are the second and fourth marks?
Steps only
Each step is 1/5.
Count two and four steps from zero.
Answer
2/5 and 4/5.
Question 3
Name the first three marks after zero when each unit is divided into eighths.
Steps only
Count one, two and three intervals of size 1/8.
Answer
1/8, 2/8 and 3/8.
Question 4
Where should 1/10, 3/10 and 4/5 be placed between 0 and 1?
Steps only
Divide 0–1 into 10 equal steps.
Mark the first step, third step and eighth step because 4/5=8/10.
Answer
At 1/10, 3/10 and 8/10 (which is 4/5), respectively.
Question 5
How many fractions lie between 0 and 1?
Steps only
Between any two different numbers, you can find another by taking their average.
Repeat this process between 0 and the new fraction.
Answer
Infinitely many. For example, between 0 and 1 are 1/2, then between 0 and 1/2 is 1/4, and this can continue forever.
Question 6
A number line has half-unit steps. What is the length of the black line ending at the third half mark?
Steps only
Each interval is 1/2.
Three intervals give 3×1/2.
Answer
3/2 units.
Question 7
What fractions name the black line endpoints at the sixth, seventh, eighth and ninth fifth-mark?
Steps only
Count fifth-size steps from zero, including the steps after 1.
Answer
6/5, 7/5, 8/5 and 9/5.
Question 8
Give five fractions of your choice and mark them between 0 and 1.
Steps only
Choose five different proper fractions, for example 1/5, 1/3, 1/2, 3/4 and 9/10.
Place them in increasing order along the line.
Answer
One possible set from left to right is 1/5, 1/3, 1/2, 3/4, 9/10. Many answers are correct.
7.5 Mixed Fractions
Textbook pages 161–163
Question 1
How many whole units are in 7/2?
Steps only
2/2 makes one whole.
7/2=3 wholes and 1/2 left.
Answer
3 whole units.
Question 2(a)
How many whole units are in 4/3?
Steps only
3 thirds make one whole, with 1 third remaining.
Answer
1 whole unit.
Question 2(b)
How many whole units are in 7/3?
Steps only
6/3=2 wholes, with 1/3 remaining.
Answer
2 whole units.
Question 3(a)
Write 8/3 as a mixed number.
Steps only
8÷3=2 remainder 2.
Answer
2 2/3.
Question 3(b)
Write 11/5 as a mixed number.
Steps only
11÷5=2 remainder 1.
Answer
2 1/5.
Question 3(c)
Write 9/4 as a mixed number.
Steps only
9÷4=2 remainder 1.
Answer
2 1/4.
Question 4
Can every fraction above one be written as a mixed number?
Steps only
A mixed number has a whole part and a proper fractional part.
For example, 8/4=2 exactly, with no fraction left.
Answer
No. An improper fraction that is exactly a whole number, such as 8/4=2, has no nonzero fractional part.
Question 5(a)
Write 9/2 as a mixed number.
Steps only
9÷2=4 remainder 1.
Answer
4 1/2.
Question 5(b)
Write 9/5 as a mixed number.
Steps only
9÷5=1 remainder 4.
Answer
1 4/5.
Question 5(c)
Write 21/19 as a mixed number.
Steps only
21÷19=1 remainder 2.
Answer
1 2/19.
Question 5(d)
Write 47/9 as a mixed number.
Steps only
47÷9=5 remainder 2.
Answer
5 2/9.
Question 5(e)
Write 12/11 as a mixed number.
Steps only
12÷11=1 remainder 1.
Answer
1 1/11.
Question 5(f)
Write 19/6 as a mixed number.
Steps only
19÷6=3 remainder 1.
Answer
3 1/6.
Question 6(a)
Write 3 1/4 as an improper fraction.
Steps only
3 wholes are 12 quarters.
12/4+1/4=13/4.
Answer
13/4.
Question 6(b)
Write 7 2/3 as an improper fraction.
Steps only
7 wholes are 21 thirds.
21/3+2/3=23/3.
Answer
23/3.
Question 6(c)
Write 9 4/9 as an improper fraction.
Steps only
9×9+4=85.
Answer
85/9.
Question 6(d)
Write 3 1/6 as an improper fraction.
Steps only
3×6+1=19.
Answer
19/6.
Question 6(e)
Write 2 3/11 as an improper fraction.
Steps only
2×11+3=25.
Answer
25/11.
Question 6(f)
Write 3 9/10 as an improper fraction.
Steps only
3×10+9=39.
Answer
39/10.
7.6 Equivalent Fractions
Textbook pages 164–173
Question 1(a)
Are 1/2 and 3/6 equal?
Steps only
1/2=3/6 after multiplying top and bottom by 3.
Answer
Yes, they have equal length and value.
Question fraction-strip-equivalence
Use a paper strip to check whether 1/3 and 2/6 have the same length.
Steps only
Divide one strip into 3 equal parts and shade one.
Divide an equal strip into 6 equal parts and shade two.
The shaded lengths match.
Answer
Yes. 1/3=2/6 because both cover the same length.
Question 1(b)
Are 2/3 and 4/6 equivalent?
Steps only
2/3×2/2=4/6.
Answer
Yes.
Question 1(c)
How many sixth-length pieces make 1/2?
Steps only
1/2=3/6.
Answer
Three pieces of length 1/6.
Question 1(d)
How many sixth-length pieces make 1/3?
Steps only
1/3=2/6.
Answer
Two pieces of length 1/6.
Question 2
Are 3/6, 4/8 and 5/10 equivalent?
Steps only
Each simplifies to 1/2.
Answer
Yes; all are equal to 1/2.
Question 3
Give two fractions equivalent to 2/6.
Steps only
Multiply numerator and denominator by 2, then by 3.
Answer
4/12 and 6/18 (also 1/3 in simplest form).
Question 4
Write 17/51 in lowest terms.
Steps only
Divide numerator and denominator by 17.
Answer
1/3.
Question 5
Write 64/144 in lowest terms.
Steps only
Divide both by 16: 64÷16=4, 144÷16=9.
Answer
4/9.
Question 6
Write 126/147 in lowest terms.
Steps only
Divide both by 21.
Answer
6/7.
Question 7
Write 525/112 in lowest terms.
Steps only
Both numbers divide by 7: 525÷7=75 and 112÷7=16.
Answer
75/16.
Question 8
Three rotis are shared equally among four children. What fraction does each child receive? State a division and addition fact.
Steps only
3÷4=3/4.
Check by adding four equal shares: 4×3/4=3 rotis.
Answer
Each child gets 3/4 roti; 3÷4=3/4 and 3/4+3/4+3/4+3/4=3.
Question 9
Two rotis are shared equally among four children. What fraction does each child receive?
Steps only
2÷4=2/4=1/2.
Four halves total 2 rotis.
Answer
Each child gets 1/2 roti.
Question 10
Two cakes are shared equally among five children. What share does each child get?
Steps only
2÷5=2/5.
Answer
2/5 cake each.
Question 11(a)
Five glasses shared by four friends gives the same share as how many glasses shared by eight friends?
Steps only
To double the number of friends and keep each share the same, double the glasses: 5/4=10/8.
Answer
10 glasses.
Question 11(b)
Four kilograms shared among three bags is the same share as 12 kg shared among how many bags?
Steps only
4/3=12/x.
The amount is tripled, so the number of bags must be tripled: 3×3=9.
Answer
9 bags.
Question 11(c)
Give another equal-share situation equivalent to 7 rotis shared among 5 children.
Steps only
Multiply both counts by the same number, such as 2.
Answer
14 rotis shared among 10 children is one example.
Question 12
If the number of children stays fixed but more whole units are shared, how does each child’s share change?
Steps only
More units are divided among the same number of children.
Answer
Each child gets a larger share.
Question 13(a)
Which gives more juice per child: 3 glasses shared among 4 children, or 7 among 10?
Steps only
Compare 3/4 and 7/10 using denominator 20: 15/20 and 14/20.
Answer
3 glasses among 4 children gives more: 3/4 > 7/10.
Question 13(b)
Which gives more per child: 4 glasses among 7 children, or 5 among 7?
Steps only
The denominators match; compare numerators 4 and 5.
Answer
5 glasses among 7 gives more: 5/7 > 4/7.
Question 13(c)
Why is it easier to compare 4/7 and 5/7 than 3/4 and 7/10?
Steps only
4/7 and 5/7 have the same denominator, so both are measured in sevenths.
For 3/4 and 7/10, first rename them with a shared denominator such as 20.
Answer
The second pair in the activity is easier because both shares use the same number of children, so the denominators already match.
Question 14
How do you make two fractions have the same fractional unit?
Steps only
Find a common multiple of the denominators.
Multiply each numerator and denominator to reach that denominator.
Answer
For example, 3/5 and 7/8 become 24/40 and 35/40 using denominator 40.
Question 15
Why does increasing the number of equal parts in a whole make each part smaller?
Steps only
The same whole is divided into more equal shares.
Answer
Each share is smaller because the whole is split into more pieces.
Question 16
Write as many fractions as you can that are equivalent to 4/6.
Steps only
First simplify: 4/6=2/3.
Multiply numerator and denominator of 2/3 by the same whole number.
Answer
Examples: 2/3=4/6=6/9=8/12=10/15=12/18=….
Question same-unit-a
Write equivalent fractions for 7/2 and 3/5 with a common denominator.
Steps only
Use 2×5=10.
7/2=35/10 and 3/5=6/10.
Answer
35/10 and 6/10.
Question same-unit-b
Write equivalent fractions for 8/3 and 5/6 with a common denominator.
Steps only
Use denominator 6.
8/3=16/6; 5/6 stays 5/6.
Answer
16/6 and 5/6.
Question same-unit-c
Write equivalent fractions for 3/4 and 3/5 with a common denominator.
Steps only
Use denominator 20.
3/4=15/20 and 3/5=12/20.
Answer
15/20 and 12/20.
Question same-unit-d
Write equivalent fractions for 6/7 and 8/5 with a common denominator.
Steps only
Use denominator 35.
6/7=30/35; 8/5=56/35.
Answer
30/35 and 56/35.
Question same-unit-e
Write equivalent fractions for 9/4 and 5/2 with a common denominator.
Steps only
Use denominator 4.
9/4 stays 9/4; 5/2=10/4.
Answer
9/4 and 10/4.
Question same-unit-f
Write equivalent fractions for 1/10 and 2/9 with a common denominator.
Steps only
Use denominator 90.
1/10=9/90; 2/9=20/90.
Answer
9/90 and 20/90.
Question same-unit-g
Write equivalent fractions for 8/3 and 11/4 with a common denominator.
Steps only
Use denominator 12.
8/3=32/12; 11/4=33/12.
Answer
32/12 and 33/12.
Question same-unit-h
Write equivalent fractions for 13/6 and 1/9 with a common denominator.
Steps only
Use denominator 18.
13/6=39/18; 1/9=2/18.
Answer
39/18 and 2/18.
7.7 Comparing Fractions
Textbook pages 173–174
Question 1(a)
Compare 8/3 and 5/2.
Steps only
A common denominator is 6: 16/6 and 15/6.
Answer
8/3 > 5/2.
Question 1(b)
Compare 4/9 and 3/7.
Steps only
A common denominator is 63: 28/63 and 27/63.
Answer
4/9 > 3/7.
Question 1(c)
Compare 7/10 and 9/14.
Steps only
A common denominator is 70: 49/70 and 45/70.
Answer
7/10 > 9/14.
Question 1(d)
Compare 12/5 and 8/5.
Steps only
The denominators already match.
12>8.
Answer
12/5 > 8/5.
Question 1(e)
Compare 9/4 and 5/2.
Steps only
Use denominator 4: 9/4 and 10/4.
Answer
9/4 < 5/2.
Question 2(a)
Put 7/10, 11/15 and 2/5 in ascending order.
Steps only
Use denominator 30: 21/30, 22/30 and 12/30.
Answer
2/5 < 7/10 < 11/15.
Question 2(b)
Put 19/24, 5/6 and 7/12 in ascending order.
Steps only
Use denominator 24: 19/24, 20/24 and 14/24.
Answer
7/12 < 19/24 < 5/6.
Question 3(a)
Put 25/16, 7/8, 13/4 and 17/32 in descending order.
Steps only
Use denominator 32: 50/32, 28/32, 104/32 and 17/32.
Answer
13/4 > 25/16 > 7/8 > 17/32.
Question 3(b)
Put 3/4, 12/5, 7/12 and 5/4 in descending order.
Steps only
Use denominator 60: 45/60, 144/60, 35/60 and 75/60.
Answer
12/5 > 5/4 > 3/4 > 7/12.
7.8 Addition and Subtraction of Fractions
Textbook pages 175–181
Question 1(a)
Find 2/7+5/7+6/7.
Steps only
The fractional unit is the same, so add numerators: 2+5+6=13.
Answer
13/7=1 6/7.
Question 1(b)
Find 3/4+1/3.
Steps only
Common denominator 12: 3/4=9/12 and 1/3=4/12.
9/12+4/12=13/12.
Answer
13/12=1 1/12.
Question 1(c)
Find 2/3+5/6.
Steps only
2/3=4/6.
4/6+5/6=9/6=3/2.
Answer
1 1/2.
Question 1(d)
Find 2/3+2/7.
Steps only
Common denominator 21: 14/21+6/21.
Answer
20/21.
Question 1(e)
Find 3/4+1/3+1/5.
Steps only
Common denominator 60: 45/60+20/60+12/60.
Add the numerators: 77.
Answer
77/60=1 17/60.
Question 1(f)
Find 2/3+4/5.
Steps only
Common denominator 15: 10/15+12/15=22/15.
Answer
22/15=1 7/15.
Question 1(g)
Find 4/5+2/3.
Steps only
Common denominator 15: 12/15+10/15.
Answer
22/15=1 7/15.
Question 1(h)
Find 3/5+5/8.
Steps only
Common denominator 40: 24/40+25/40.
Answer
49/40=1 9/40.
Question 1(i)
Find 9/2+5/4.
Steps only
9/2=18/4.
18/4+5/4=23/4.
Answer
5 3/4.
Question 1(j)
Find 8/3+2/7.
Steps only
Common denominator 21: 56/21+6/21.
Answer
62/21=2 20/21.
Question 1(k)
Find 3/4+1/3+1/5.
Steps only
Common denominator 60: 45/60+20/60+12/60.
Answer
77/60=1 17/60.
Question 1(l)
Find 2/3+4/5+3/7.
Steps only
Common denominator 105: 70/105+84/105+45/105.
Add: 199/105.
Answer
199/105=1 94/105.
Question 1(m)
Find 9/2+5/4+7/6.
Steps only
Common denominator 12: 54/12+15/12+14/12.
Add: 83/12.
Answer
83/12=6 11/12.
Question 2
Rahim mixes 2/3 L yellow paint with 3/4 L blue paint. How much paint is there?
Steps only
Common denominator 12: 8/12+9/12=17/12.
Answer
1 5/12 L.
Question 3
Geeta has 2/5 m of lace and Shamim has 3/4 m. Is the total enough for a 1 m border?
Steps only
Common denominator 20: 8/20+15/20=23/20=1 3/20 m.
1 3/20 m is longer than 1 m.
Answer
Yes. They have 1 3/20 m, which is 3/20 m more than needed.
Question 4(a)
Find 5/8−3/8.
Steps only
Subtract the numerators: 5−3=2.
2/8=1/4.
Answer
1/4.
Question 4(b)
Find 7/9−5/9.
Steps only
7−5=2.
Answer
2/9.
Question 4(c)
Find 10/27−1/27.
Steps only
10−1=9.
9/27=1/3.
Answer
1/3.
Question 5(a)
Find 8/15−3/15.
Steps only
Same denominator: (8−3)/15.
Answer
1/3.
Question 5(b)
Find 2/5−4/15.
Steps only
Convert 2/5 to 6/15.
6/15−4/15=2/15.
Answer
2/15.
Question 5(c)
Find 5/6−4/9.
Steps only
Common denominator 18: 15/18−8/18.
Answer
7/18.
Question 5(d)
Find 2/3−1/2.
Steps only
Common denominator 6: 4/6−3/6.
Answer
1/6.
Question 6(a)
Subtract 13/4 from 10/3.
Steps only
Common denominator 12: 10/3=40/12 and 13/4=39/12.
40/12−39/12=1/12.
Answer
1/12.
Question 6(b)
Subtract 18/5 from 23/3.
Steps only
Common denominator 15: 23/3=115/15 and 18/5=54/15.
115/15−54/15=61/15.
Answer
4 1/15.
Question 6(c)
Subtract 29/7 from 45/7.
Steps only
(45−29)/7=16/7.
Answer
2 2/7.
Question 7(a)
Jaya’s school is 7/10 km away. She travels 1/2 km by auto. How far does she walk?
Steps only
1/2=5/10.
7/10−5/10=2/10=1/5 km.
Answer
She walks 1/5 km.
Question 7(b)
Jeevika takes 10/3 minutes for a lap; Namit takes 13/4 minutes. Who is quicker and by how much?
Steps only
10/3=40/12 and 13/4=39/12.
Difference=1/12 minute.
Answer
Namit is quicker by 1/12 minute.
Question worked-chikki-add
Meena eats 1/2 of a chikki and her brother eats 1/4. How much do they eat together, and how much remains?
Steps only
Rewrite 1/2 as 2/4.
Together: 2/4+1/4=3/4.
Remaining: 1−3/4=1/4.
Answer
They eat 3/4 of the chikki, so 1/4 remains.
Question worked-same-unit-add
Find 2/5+1/5 and 4/7+6/7.
Steps only
For fifths: 2/5+1/5=3/5.
For sevenths: 4/7+6/7=10/7=1 3/7.
Answer
The sums are 3/5 and 1 3/7.
Question worked-different-unit-add
Find 1/4+1/3, 2/3+1/5 and 1/6+1/3.
Steps only
1/4+1/3=3/12+4/12=7/12.
2/3+1/5=10/15+3/15=13/15.
1/6+1/3=1/6+2/6=3/6=1/2.
Answer
The sums are 7/12, 13/15 and 1/2.
Question worked-same-unit-subtract
What is 6/7−4/7?
Steps only
Remove four of the six seventh-sized parts.
6/7−4/7=2/7.
Answer
2/7.
Question worked-different-unit-subtract
Find 3/4−2/3.
Steps only
Use twelfths: 3/4=9/12 and 2/3=8/12.
9/12−8/12=1/12.
Answer
1/12.
7.9 A Pinch of History and Fraction Puzzles
Textbook pages 182–185
Question history-notation
What does “bhinna” mean, and where did the fraction notation used today originate?
Steps only
“Bhinna” means broken; “bhaga” or “ansha” means part or piece.
The chapter explains that the notation for fractions we use today originated in India.
Answer
“Bhinna” means broken, and the text traces today’s fraction notation to India before it spread more widely.
Question different-unit-pairs
Can two different unit fractions add to exactly 1? Explain why or why not.
Steps only
The largest unit fraction is 1/2.
If the two unit fractions are different, at least one is smaller than 1/2; the other is at most 1/2.
Their sum must therefore be less than 1.
Answer
No. Two different unit fractions cannot add to 1.
Question three-distinct-units
Find three different unit fractions whose sum is 1.
Steps only
Start with 1/2+1/3=5/6.
The missing part is 1−5/6=1/6.
Answer
1/2+1/3+1/6=1.
Question four-distinct-units
Find all six sets of four different unit fractions that add to 1.
Steps only
For example, 1/2+1/3 leaves 1/6; split 1/6 into two distinct unit fractions in each possible way.
Other starting pairs give the remaining cases. Verify each sum with a common denominator.
Answer
The six sets are: 1/2+1/3+1/7+1/42; 1/2+1/3+1/8+1/24; 1/2+1/3+1/9+1/18; 1/2+1/3+1/10+1/15; 1/2+1/4+1/5+1/20; and 1/2+1/4+1/6+1/12.