Four friends want to share 3 pizzas equally. How much pizza does each person get?
A4/3 of a pizza — there are more people than pizzas, so each person gets more than one pizza's worth
B3/4 of a pizza — because 3 divided by 4 equals 3/4
C1 pizza each — you round up when the division doesn't come out evenly
DThis problem can't be solved because 4 doesn't divide evenly into 3
3 pizzas ÷ 4 people = 3/4 of a pizza each. The fraction 3/4 IS the division problem 3 ÷ 4 — the fraction bar means divide. Option D is the classic misconception this topic directly overturns: division always produces a valid answer, and when the dividend is smaller than the divisor, the answer is a fraction less than 1. Option A confuses the number of people (4) with the denominator — the denominator is 4 because that's what you divide BY.
Question 2 Multiple Choice
Which expression is equivalent to the fraction 7/8?
A8 ÷ 7
B7 × 8
C7 ÷ 8
D8 − 7
The fraction a/b means a ÷ b — the numerator is divided by the denominator. So 7/8 = 7 ÷ 8. Option A (8 ÷ 7) is the most tempting wrong answer: students who know that fractions involve division but are unsure of the direction often flip the numerator and denominator. Remember: the number on top (numerator) is what gets divided, and the number on the bottom (denominator) is what you divide by.
Question 3 True / False
To convert the fraction 5/8 to a decimal, you should divide 8 by 5.
TTrue
FFalse
Answer: False
The fraction 5/8 means 5 ÷ 8, not 8 ÷ 5. You always divide the numerator by the denominator. 5 ÷ 8 = 0.625. Dividing 8 ÷ 5 gives 1.6, which is a completely different number. This direction error is one of the most common mistakes when converting fractions to decimals — always ask 'what is on top?' and divide that by 'what is on the bottom.'
Question 4 True / False
The fraction 5/8 and the division expression 5 ÷ 8 represent the same number.
TTrue
FFalse
Answer: True
This is the core idea of fractions as division: the fraction bar IS a division symbol. 5/8 is an instruction meaning 'divide 5 by 8,' and the result is 0.625. Writing 5 ÷ 8 is just another way to write the same instruction. They produce the same number, and you can convert any fraction to a decimal by carrying out that division.
Question 5 Short Answer
Why does 3/4 equal 0.75? Use the fraction-as-division idea to explain step by step.
Think about your answer, then reveal below.
Model answer: The fraction 3/4 means 3 ÷ 4 — divide 3 by 4. Carrying out that long division: 4 goes into 3 zero times, so you add a decimal point and a zero to get 30. 4 goes into 30 seven times (4 × 7 = 28), remainder 2. Bring down another zero to get 20. 4 goes into 20 exactly 5 times (4 × 5 = 20), remainder 0. Result: 0.75. So 3/4 = 0.75 because performing the division that the fraction represents gives 0.75.
This is why fractions and decimals are not two separate kinds of numbers — they are two different notations for the same quantity. The fraction 3/4 is an exact representation; 0.75 is the decimal result of carrying out the implied division. Any fraction can be converted to a decimal by performing this division, which is why the fraction bar and the division symbol are functionally identical.