Chapter 2

Fractions, Decimals and Percentages

Mixed numbers in all four operations, percentage change in both directions, and the reverse question that catches almost everyone: finding the original amount.

หลักสูตรแกนกลาง / สสวท.: จำนวนและพีชคณิต (Number and Algebra)ต่อยอดจาก ม.1 บทที่ 4 ทศนิยมและเศษส่วน และบทที่ 7 ร้อยละ
Common Core (US): 7.NS, 7.RP
Cambridge: Lower Secondary Stage 8 — Number: fractions, decimals and percentages

2.1 Mixed numbers and improper fractions

The safe routine

1Convert every mixed number to an improper fraction first
2Do the arithmetic
3Convert back at the very end, if the question asks for it

ข้อควรระวัง

Multiplying mixed numbers by handling the whole parts and the fractions separately does not work. $2 \frac{1}{2} \times 3$ is $\frac{15}{2} = 7 \frac{1}{2}$ , not $6 \frac{1}{2}$ — the whole number multiplies the fraction part too.

ตัวอย่าง

Work out $2 \frac{3}{4} \div 1 \frac{1}{2}$

วิธีทำ

1.Improper first: $\frac{11}{4} \div \frac{3}{2}$
2.Dividing means multiplying by the reciprocal: $\frac{11}{4} \times \frac{2}{3}$
3. $= \frac{22}{12} = \frac{11}{6}$

ตอบ $1 \frac{5}{6}$

เคล็ดลับ

Recurring decimals show up here: $\frac{1}{3} = 0.333 \dots$ is written $0. \overline{3}$ . A fraction always gives a decimal that either stops or repeats — it can never do neither.

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