7.2 Directed Numbers

Maria places -2 on a number line. She says it is 3 steps to the right of -5. Is she correct? Justify using the number line.

Which is greater, -7 or -3? Justify by describing their positions on a number line.

Two negative integers add to -12. Give one possible pair and justify that both numbers are negative and their sum is correct.

The temperature is 3°C. It falls by 10°C. What is the new temperature? Explain which direction the fall takes you on a number line.

Bob says "-6 × 4 = 24". Spot the error and give the correct answer with a reason.

If 18 ÷ 3 = 6, what is 18 ÷ (−3)? Justify using the sign rules.

A bank account has £20. The account holder spends £35. What is the new balance and what does the negative sign mean in context?

What is the distance between -4 and 7 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 15 m below sea level (so their position is −15 m). They rise 8 m. Write a calculation and find the new position.

Write in order from smallest to largest: -9, 4, -1, -6, 0.

Calculate -8 + 5 + -3.

Calculate -2 − (-9).

Calculate -14 + 6, then subtract -3 from your answer.

Calculate -4 × 3 + 15.

Calculate -24 ÷ 6 − 2.

The temperature starts at -3°C and falls by 8°C overnight. By midday it has risen 14°C. What is the midday temperature?

Find the value of $\square$ if $\square + (-6) = -2$.

Find the midpoint of -8 and 4 on a number line.

A bank account holds £15. Two payments of £23 and £7 are debited. What is the new balance?

Find the LCM of 12 and 18. State whether your answer is positive or negative, and explain why.

Evaluate $(-5)^2$. Then evaluate $(5)^2$. What do you notice?

Work out $-3 \times 5 + 18 \div (-6)$.

Two integers multiply to give -15. One integer is 5. Find the other integer.

Work out $(-8 + 3) \times (-2)$.

Evaluate $-(5^2) + 30$.

A submarine is at 80 m below sea level. It rises 35 m. What is its new depth? (Use a negative number to represent depth below sea level.)

Find the HCF of 18 and 24. A diver records two temperatures: −(HCF)°C and +(HCF)°C. What is the difference between the warmer and colder temperatures?

Evaluate $(-2)^3 + (-1)^2$.

Start with -12. Add 8. Then multiply the result by -2.

Two negative integers multiply to give 36. Their sum is -13. Find both integers.

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

Two integers have product -20 and sum -1. Find both integers.

Write 36 as a product of prime factors. Call this result $p$. Now evaluate $p \div (-4)$.

Find the LCM of 4 and 6. Call it $n$. Calculate $-n^2$.

A sequence begins -25, -19, -13, -7, … and increases by a constant amount each time. Find the 10th term.

Solve $x^2 = 25$. For each solution $x$, calculate $x^2 - 5x$.

A temperature starts at -18°C. It rises by the LCM of 4 and 6 degrees. What is the final temperature?

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

Evaluate $(-3)^2 - 4 \times (-5) + 18 \div (-6)$.