Unit 1 · Class 7 IB MYP · MCQ Test
Rational Numbers MCQ Test — Class 7 IB MYP
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Rational Numbers — MCQ Questions
1The number line below shows points P, Q, R, and S. Which point correctly represents the fraction 3/4?
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Answer: R
Hint: Consider dividing the space between 0 and 1 into equal parts to locate fractions.
Solution:
Identify the total number of equal segments between 0 and 1. There are 4 segments. — Segments = 4
Each segment represents 1/4 of the whole. Count 3 segments from 0. — Point R is at the 3rd mark out of 4, representing 3/4.
Therefore, point R correctly represents 3/4.
2A point P is located on a number line between 0 and 1. If the line segment from 0 to 1 is divided into 8 equal parts, and P is at the 5th mark from 0, what rational number does point P represent?
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Answer: 5/8
Hint: Think about how many equal parts the whole is divided into and which specific part P represents.
Solution:
The entire segment from 0 to 1 is divided into 8 equal parts, so each part represents 1/8 of the whole.
Point P is at the 5th mark from 0. This means it represents 5 of these 8 equal parts. — 5 × (1/8) = 5/8
Therefore, the rational number represented by point P is 5/8.
3A chef is scaling a recipe. If 3/4 cup of flour is needed for a small batch, which of the following represents an equivalent amount for a larger batch?
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Answer: 6/8 cups
Hint: To find an equivalent fraction, multiply both the numerator and the denominator by the same non-zero integer.
Solution:
The original amount of flour is 3/4 cup.
To find an equivalent fraction, we can multiply the numerator and denominator by the same number. Let's try multiplying by 2: — (3 × 2) / (4 × 2) = 6/8
Checking the options, 6/8 cups is an equivalent amount.
4Elena spent 1/3 of an hour travelling to school and then 1/4 of an hour travelling to her sports practice in Berlin. What is the total fraction of an hour she spent travelling?
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Answer: 7/12
Hint: Remember to find a common denominator before adding fractions with different denominators.
Solution:
To find the total time, we need to add the two fractions: 1/3 + 1/4.
The least common multiple (LCM) of the denominators 3 and 4 is 12.
Convert each fraction to an equivalent fraction with a denominator of 12: — 1/3 = (1 × 4) / (3 × 4) = 4/12 1/4 = (1 × 3) / (4 × 3) = 3/12
Now, add the equivalent fractions: — 4/12 + 3/12 = (4 + 3) / 12 = 7/12
5Calculate the value of 7/8 - 1/2.
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Answer: 3/8
Hint: To subtract fractions with different denominators, first find a common denominator.
Solution:
The fractions are 7/8 and 1/2. The least common multiple (LCM) of 8 and 2 is 8.
Convert 1/2 to an equivalent fraction with a denominator of 8: — 1/2 = (1 × 4) / (2 × 4) = 4/8
Now, subtract the equivalent fractions: — 7/8 - 4/8 = (7 - 4) / 8 = 3/8
6A nature reserve in Kenya covers 5/6 of a certain region. If 2/3 of this reserve is designated for wildlife conservation, what fraction of the total region is designated for wildlife conservation?
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Answer: 5/9
Hint: When you need to find a 'fraction of a fraction', you usually perform multiplication.
Solution:
The reserve covers 5/6 of the region.
2/3 of this reserve is for conservation. To find what fraction of the total region this is, we multiply the two fractions: — (5/6) × (2/3)
Multiply the numerators and the denominators: — (5 × 2) / (6 × 3) = 10/18
Simplify the resulting fraction by dividing both numerator and denominator by their greatest common divisor, which is 2: — 10/18 = (10 ÷ 2) / (18 ÷ 2) = 5/9
7A baker has 3/4 kg of dough. If each loaf of bread requires 1/8 kg of dough, how many loaves can the baker make?
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Answer: 6 loaves
Hint: To find out how many times one fraction fits into another, you should divide.
Solution:
To find the number of loaves, divide the total amount of dough by the amount needed per loaf: — (3/4) ÷ (1/8)
To divide by a fraction, multiply by its reciprocal (flip the second fraction): — (3/4) × (8/1)
Multiply the numerators and denominators: — (3 × 8) / (4 × 1) = 24/4
Simplify the fraction: — 24/4 = 6
8Evaluate: (1/2 + 1/4) × 2/3.
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Answer: 1/2
Hint: Remember to follow the order of operations (PEMDAS/BODMAS). Start with the operation inside the parentheses.
Solution:
First, solve the expression inside the parentheses: 1/2 + 1/4. Find a common denominator, which is 4. — 1/2 = 2/4
Add the fractions inside the parentheses: — 2/4 + 1/4 = 3/4
Now, multiply the result by 2/3: — (3/4) × (2/3)
Multiply the numerators and denominators: — (3 × 2) / (4 × 3) = 6/12
Simplify the fraction by dividing both numerator and denominator by 6: — 6/12 = 1/2
9A scientist measures a chemical reaction that completes in 3/5 of a second. Express this time as a decimal.
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Answer: 0.6
Hint: To convert a fraction to a decimal, divide the numerator by the denominator.
Solution:
The fraction is 3/5.
To convert it to a decimal, divide the numerator (3) by the denominator (5): — 3 ÷ 5
Performing the division gives 0.6. — 3 ÷ 5 = 0.6
10Three athletes ran different portions of a relay race: Athlete A ran 1/2 of the track, Athlete B ran 3/8 of the track, and Athlete C ran 3/4 of the track. Which list shows the athletes in order from the smallest portion of the track run to the largest?
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Answer: Athlete B, Athlete A, Athlete C
Hint: Convert all fractions to a common denominator to make comparison easier, or convert them to decimals.
Solution:
The portions run are: Athlete A = 1/2, Athlete B = 3/8, Athlete C = 3/4.
To compare them, find a common denominator. The least common multiple (LCM) of 2, 8, and 4 is 8.
Convert each fraction to an equivalent fraction with a denominator of 8: — Athlete A: 1/2 = (1 × 4) / (2 × 4) = 4/8 Athlete B: 3/8 (already has denominator 8) Athlete C: 3/4 = (3 × 2) / (4 × 2) = 6/8
Now, compare the numerators: 3/8 (Athlete B), 4/8 (Athlete A), 6/8 (Athlete C). — 3/8 < 4/8 < 6/8
The order from smallest to largest is Athlete B, Athlete A, Athlete C.
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Tips for Rational Numbers MCQs
- 1Read each question carefully and identify what is being asked before looking at the options.
- 2Try to solve the problem mentally or on paper first, then match your answer with the options.
- 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
- 4Check units, signs, and edge cases — these are common traps in Rational Numbers MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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