7.2 Directed Numbers

Maria places 1 on a number line. She says it is 5 steps to the right of -4. Is she correct? Justify using the number line.

Which is greater, -10 or -6? Justify by describing their positions on a number line.

Two negative integers add to -15. Give one possible pair and justify that both numbers are negative and their sum is correct.

The temperature is 5°C. It falls by 14°C. What is the new temperature? Explain which direction the fall takes you on a number line.

Bob says "-7 × 5 = 35". Spot the error and give the correct answer with a reason.

If 20 ÷ 4 = 5, what is 20 ÷ (−4)? Justify using the sign rules.

A bank account has £30. The account holder spends £47. What is the new balance and what does the negative sign mean in context?

What is the distance between -6 and 5 on a number line? Show your method.

Sam says "negative × negative = negative". Is Sam correct? Give an example and a counter-example if needed.

A diver is at 20 m below sea level (so their position is −20 m). They rise 13 m. Write a calculation and find the new position.

Write in order from smallest to largest: -12, 7, -3, -8, 2.

Calculate -12 + 7 + -4.

Calculate -5 − (-13).

Calculate -20 + 8, then subtract -5 from your answer.

Calculate -5 × 4 + 26.

Calculate -35 ÷ 7 − 3.

The temperature starts at -7°C and falls by 9°C overnight. By midday it has risen 20°C. What is the midday temperature?

Find the value of $\square$ if $\square + (-9) = -3$.

Find the midpoint of -10 and 2 on a number line.

A bank account holds £20. Two payments of £31 and £12 are debited. What is the new balance?

Find the LCM of 8 and 20. State whether your answer is positive or negative, and explain why.

Evaluate $(-7)^2$. Then evaluate $(7)^2$. What do you notice?

Work out $-4 \times 7 + 30 \div (-5)$.

Two integers multiply to give -24. One integer is 6. Find the other integer.

Work out $(-6 + 2) \times (-3)$.

Evaluate $-(4^2) + 20$.

A submarine is at 120 m below sea level. It rises 65 m. What is its new depth? (Use a negative number to represent depth below sea level.)

Find the HCF of 20 and 28. A diver records two temperatures: −(HCF)°C and +(HCF)°C. What is the difference between the warmer and colder temperatures?

Evaluate $(-3)^3 + (-2)^2$.

Start with -15. Add 9. Then multiply the result by -3.

Two negative integers multiply to give 24. Their sum is -10. Find both integers.

Evaluate $(-3)^4 - (-2)^3$.

Two integers have product -30 and sum 1. Find both integers.

Write 40 as a product of prime factors. Call this result $p$. Now evaluate $p \div (-5)$.

Find the LCM of 4 and 10. Call it $n$. Calculate $-n^2$.

A sequence begins -30, -23, -16, -9, … and increases by a constant amount each time. Find the 10th term.

Solve $x^2 = 36$. For each solution $x$, calculate $x^2 - 6x$.

A temperature starts at -25°C. It rises by the LCM of 6 and 10 degrees. What is the final temperature?

Let $a$ be negative and $b$ be negative. State whether each expression is positive, negative, or could be either: (i) $a \times b$, (ii) $a + b$, (iii) $a \div b$.

Evaluate $(-4)^2 - 3 \times (-7) + 20 \div (-4)$.