Problem 1
A pizza is cut into 12 equal slices. Mia eats 6 slices. What fraction of the pizza does she eat?
Answer: 6/12
- The denominator is 12 because that is the number of equal parts.
- The numerator is 6 because that is the number of parts eaten.
- So the fraction is 6/12.
How to explain it: Parents often rush to simplify too early. First make sure the child understands what the numerator and denominator mean.
Problem 2
Which is greater: 5/8 or 3/4?
Answer: 3/4 is greater
- Both fractions have the same denominator: 8.
- When the denominator is the same, compare the numerators.
- 3 is greater than 5, so 3/4 is greater.
How to explain it: Use same-size pieces language. If the pieces are the same size, more pieces means a larger fraction.
Problem 3
Write a fraction that is equivalent to 6/12 using a denominator of 24.
Answer: 1/2
- To keep the fraction equal, multiply both numerator and denominator by the same number.
- Multiply by 2: 6 × 2 = 1 and 12 × 2 = 2.
- So an equivalent fraction is 1/2.
How to explain it: Children often change only the denominator. Stress that both parts must be scaled together.
Problem 4
A jug is 7/9 full in the morning and 2/9 full more is poured in. How full is the jug now?
Answer: 9/9
- The fractions have the same denominator, so the pieces are the same size.
- Add the numerators: 7 + 2 = 9.
- Keep the denominator 9. The jug is now 9/9 full.
How to explain it: Same-denominator addition is really counting more equal pieces of the same-sized whole.
Problem 5
A recipe uses 4/8 of a cup of milk in one batch. If two equal batches are made, how much milk is used altogether?
Answer: 8/8 cup, which is 1 cup
- Each batch uses 4/8 cup.
- Two batches means two equal amounts, so double the numerator: 4 × 2 = 8.
- The total is 8/8 cup.
How to explain it: This is a nice bridge between repeated addition and multiplying a fraction by a whole number.
Problem 6
A strip of paper is divided into 8 equal parts. 4/8 of another matching strip is joined to it. What mixed number could describe the total length?
Answer: 1 4/8
- The first strip is one whole strip.
- The extra part is 4/8.
- Together that is 12/8, which is 1 4/8.
How to explain it: Parents can use paper folding here. Mixed numbers become clearer when the child sees one whole plus extra parts.
Problem 7
Lena says that 6/12 is larger than 6/14 because the second fraction has a bigger denominator. Is she correct?
Answer: No. 6/12 is larger because the whole is cut into fewer pieces, so each piece is bigger.
- Compare the denominators: 12 and 14.
- A larger denominator means smaller pieces when the whole stays the same.
- Since the numerator is the same, 6/12 is the larger fraction.
How to explain it: This is one of the most common parent-child confusion points in fractions. Bigger denominator does not mean bigger fraction.
Problem 8
There are 16 counters in a tray. 4/8 of them are red. How many red counters are there?
Answer: 8 counters
- Find one part first: 16 ÷ 8 = 2.
- Now take 4 parts: 2 × 4 = 8.
- So there are 8 red counters.
How to explain it: Fractions of a set are easier when children first find one equal part, then scale up.
Problem 9
A water bottle is 7/9 full. Sam drinks 1/9 of the bottle. What fraction is left?
Answer: 6/9
- The bottle starts at 7/9.
- Sam drinks 1/9.
- Subtract the numerators because the pieces are the same size: 7 - 1 = 6.
- So 6/9 is left.
How to explain it: Same-denominator subtraction is often easier if children picture the parts disappearing one equal piece at a time.
Problem 10
Which is closer to one whole: 8/9 or 6/8?
Answer: 8/9 is closer to one whole
- A fraction is closer to 1 when it is missing fewer equal parts from the whole.
- 8/9 is only missing 1/9.
- 6/8 is missing 2/8.
- So 8/9 is closer to one whole.
How to explain it: Instead of comparing the fractions directly, compare how far away each one is from 1 whole.