☰ خطة العام · الرياضيات (بالإنجليزية)

Equations, unknown numbers and factors

الأسبوع 4 · العبارات والمعادلات والمجاهيل؛ العوامل الأولى · 3 دروس
3

Stories for equations, and the factors of a number

Discover Mathematics P5: Term 1, Unit 2, Lessons 1–5
GoalWrite an equation for a story, and list all the factors of a number.
New words
factor · a number that divides another number exactly, with no remainderfactor pair · two numbers whose product is the given number, such as 3 and 8 for 24divisible · can be divided exactly
Explanation

To write an equation for a story, choose a letter for the unknown, then say the story with numbers and the letter. “Hana had x LE, spent 18.5 LE and has 31.5 LE left” gives x − 18.5 = 31.5, so x = 31.5 + 18.5 = 50. To find the factors of a number, look for pairs of whole numbers that multiply to it. Test 1, 2, 3, … in order, writing each pair, and stop when the pairs meet. For 24: 1 × 24, 2 × 12, 3 × 8, 4 × 6. The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. Every number has 1 and itself as factors. A number such as 36 has the pair 6 × 6, so 6 is listed only once.

Factor pairProduct
1 × 2424
2 × 1224
3 × 824
4 × 624
Worked examples
A tailor cuts 2.75 m from a roll of cloth and 4.5 m remain. Let r be the length of the roll. The story says r − 2.75 = 4.5, so r = 4.5 + 2.75 = 7.25 m. Check: 7.25 − 2.75 = 4.5.
Here is a story for 3 × s = 4.5: three equal packs of rice weigh 4.5 kg altogether, and each pack weighs s kg. s = 4.5 ÷ 3 = 1.5 kg. Check: 3 × 1.5 = 4.5.
Factor pairProduct
1 × 3636
2 × 1836
3 × 1236
4 × 936
6 × 636
Find all factors of 36. Pairs: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36. That makes 9 factors. 5 is not a factor because 36 ÷ 5 leaves a remainder.
Class activity

Factor rectangles. Take 24 small squares (or draw them on squared paper). Arrange them in rectangles with no gaps: 1 by 24, 2 by 12, 3 by 8, 4 by 6. Write each pair. Try with 30 and 36 too. Which of the numbers makes a square?

Practice
1
Omar had some marbles, got 15 more and now has 42. Write an equation and solve it.
2
Solve y ÷ 4 = 7.5 and tell a short story for it.
3
List all the factors of 18.
4
Write the factor pairs of 40.
5
Is 6 a factor of 54? Is 8 a factor of 54?