Grade 7 Math — Properties of rational numbers
Add, subtract, multiply and divide rational numbers, and use the properties that make the work shorter.
Name: ________________________
Before you start
Wander along this line in quarter steps. Nothing here is right or wrong — see how the numbers crowd together.
The line only shows quarters, but between any two of them sits another rational number — an eighth, a sixteenth, and so on for ever. There is no 'next' rational number.
1.5/7 × 3/4 gives the same answer as 3/4 × 5/7. Which property is that?
- a) Multiplication of rational numbers is associative
- b) Multiplication is distributive over addition
- c) Multiplication of rational numbers is commutative
- d) One is the multiplicative identity
2.Tap where -7/4 sits.
Mark the line with an X.
3.2/3 × 9/8 = ? Write your answer as a fraction in its simplest form.
4.Write the rational number that lies exactly halfway between 1/3 and 1/2.
5.What is the reciprocal of -7/9? Write your answer as a fraction.
6.Match each rational number to its additive inverse — the number you add to it to get zero.
- 2/7
- -5/9
- 3/4
- -11/6
- 8/3
- -3/4
- -8/3
- -2/7
- 11/6
- 5/9
7.4/9 × 7/5 + 4/9 × 3/5 = ? Write your answer as a fraction.
8.Rational numbers are closed under addition, subtraction and multiplication. Which operation is the exception, because one case has no answer at all?
- a) Division, when you divide by zero
- b) Multiplication, when one number is a fraction
- c) Subtraction, when the answer comes out negative
- d) Addition, when both numbers are negative
Answer key — Grade 7 Math — Properties of rational numbers
- 1. c) Multiplication of rational numbers is commutative
- 2. -1.75
- 3. 3/4
- 4. 5/12
- 5. -9/7
- 6. 2/7 → -2/7; -5/9 → 5/9; 3/4 → -3/4; -11/6 → 11/6; 8/3 → -8/3
- 7. 8/9
- 8. a) Division, when you divide by zero