3
Finding the unknown in a comparison
Discover Mathematics P4: Term 1, Unit 5, Lessons 1–3
GoalUse a letter for the unknown number in a comparison and solve by dividing or multiplying.
New words
unknown · the number we do not know yetvariable · a letter that stands for the unknown numberinverse operation · division undoes multiplication
Explanation
Sometimes the small number is unknown. Aya has 35 stamps. She has 5 times as many as Omar. Let n be the number of Omar stamps. The equation is 35 = 5 × n. The bar model shows 5 equal bars that together make 35, so each bar is 35 ÷ 5 = 7. So n = 7. Division is the opposite of multiplication, so we divide the big number by the number of times. If the big number is unknown we multiply: a = 6 × 8 = 48. Always check by multiplying back: 5 × 7 = 35. Then write the answer in a sentence: Omar has 7 stamps.
Worked examples
Aya has 35 stamps, 5 times as many as Omar. 35 = 5 × n, so n = 35 ÷ 5 = 7. Omar has 7 stamps. Check: 5 × 7 = 35.
| Step | Work |
|---|---|
| 1 | 40 = 8 × t |
| 2 | t = 40 ÷ 8 |
| 3 | t = 5 |
Karim saved 600 LE. That is 4 times as much as his sister saved. Her savings s: 600 = 4 × s, so s = 600 ÷ 4 = 150 LE. If the sister saved 150 LE, Karim saved 4 × 150 = 600 LE. When the big number is unknown, we multiply.
Class activity
Mystery number. A grown-up thinks of a number and says: my number times 6 is 42. The child writes n × 6 = 42 and finds the number. Then the child hides a number and says a times-as-many clue for the grown-up to solve.
Practice
1
Mariam has 28 beads, 4 times as many as Hana. How many beads does Hana have?
28 = 4 × n, so n = 28 ÷ 4 = 7 beads.
2
Solve: 63 = 9 × n.
n = 63 ÷ 9 = 7.
3
A mango tree is 12 m tall. It is 3 times as tall as a guava tree. How tall is the guava tree?
12 = 3 × g, so g = 4 m.
4
A notebook costs 15 LE. A pen costs 5 LE. How many times as much is the notebook?
15 ÷ 5 = 3, so 3 times as much.
5
Youssef solves 54 = 6 × n and gets n = 9. Another student says n = 48 because 54 − 6 = 48. Who is right?
Youssef. 54 ÷ 6 = 9 and 6 × 9 = 54. The other student subtracted instead of dividing.