Fractions

Equivalence, comparison and the four operations — including the two rules students most often merge by mistake: you need a common denominator to add, but not to multiply.

หลักสูตรแกนกลาง / สสวท.: จำนวนและพีชคณิต (Number and Algebra)ตรงกับ ม.1 บทที่ 4 ทศนิยมและเศษส่วน (ส่วนเศษส่วน)
Common Core (US): 5.NF, 6.NS
Cambridge: Lower Secondary Stage 7 — Number: fractions, decimals and percentages

4.1 Equivalent fractions and simplifying

Equivalence

\frac{a}{b} = \frac{a \times k}{b \times k} = \frac{a \div k}{b \div k} (k \neq = 0)

Multiplying or dividing top and bottom by the same number changes how the fraction looks, never what it is worth.

Writing a fraction in its simplest form

1Find the HCF of the numerator and denominator
2Divide both by it
3Check nothing divides into both any more

ตัวอย่าง

Simplify $\frac{42}{56}$

วิธีทำ

1. $42 = 2 \times 3 \times 7$ and $56 = 2^{3} \times 7$
2.HCF $= 2 \times 7 = 14$
3. $42 \div 14 = 3$ and $56 \div 14 = 4$

ตอบ $\frac{3}{4}$

เคล็ดลับ

To compare fractions quickly, cross-multiply: $\frac{3}{5}$ against $\frac{5}{8}$ gives $3 \times 8 = 24$ against $5 \times 5 = 25$ , so $\frac{5}{8}$ is larger.

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