Chapter 3

Ratio, Proportion and Rates

Sharing in a ratio, telling direct from inverse proportion, and the compound measures — speed and density — that are just rates with names.

หลักสูตรแกนกลาง / สสวท.: จำนวนและพีชคณิต (Number and Algebra)ต่อยอดจาก ม.1 บทที่ 7 อัตราส่วน สัดส่วน และร้อยละ
Common Core (US): 7.RP, 6.RP
Cambridge: Lower Secondary Stage 8 — Number: ratio and proportion

3.1 Simplifying and sharing

Simplifying a ratio

1Convert to the same units first — this is the step that gets skipped
2Divide every part by their HCF
3For a ratio like $1 : n$ , divide every part by the first

ตัวอย่าง 1

Simplify the ratio $45$ minutes $: 2$ hours.

วิธีทำ

1.Same units first: $45 : 120$ minutes
2.HCF of $45$ and $120$ is $15$

ตอบ $3 : 8$

ตัวอย่าง 2

Share $6, 300$ baht in the ratio $2 : 3 : 4$ .

วิธีทำ

1.Total parts: $2 + 3 + 4 = 9$
2.One part: $6, 300 \div 9 = 700$
3.Shares: $1, 400$ , $2, 100$ , $2, 800$

ตอบ $1, 400$ , $2, 100$ and $2, 800$ baht

ข้อควรระวัง

A ratio compares part to part. In $2 : 3$ the first share is $\frac{2}{5}$ of the total, not $\frac{2}{3}$ — and this stays the defining ratio error right through to Stage 9.

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