Question

1. circle the fraction if it is equivalent to $\frac{3}{4}$. $\frac{9}{12}$ $\frac{75}{100}$ $\frac{2}{5}$ $\frac{6}{9}$ $\frac{6}{12}$ $\frac{4}{6}$ $\frac{9}{10}$ $\frac{12}{16}$ write another fraction equivalent to $\frac{3}{4}$ $\to$ 2. $25enclose{longdiv}{2,653}$ 3. solve. $42\times10=$ $42\times10^{2}=$ $42\times10^{3}=$ $42\times10^{4}=$ 4. sweet stuff bakery made 25 dozen cookies. they sold 48 of the cookies. how many cookies are left? cookies 5. write each set of fractions in order from least to greatest. $\frac{6}{8}$ $\frac{1}{12}$ $\frac{1}{8}$ $\frac{8}{4}$ $\frac{5}{8}$ $\frac{9}{8}$ $\frac{8}{6}$ $\frac{1}{3}$ $\frac{5}{6}$ $\frac{4}{6}$ $\frac{1}{2}$ $\frac{6}{6}$ $\frac{3}{8}$ $\frac{1}{4}$ $\frac{7}{4}$ $\frac{1}{2}$ $\frac{4}{4}$ $\frac{8}{4}$

Explanation:

Step1: Simplify fractions

Simplify each fraction to check equivalence with \(\frac{3}{4}\).

• \(\frac{9}{12}=\frac{9\div3}{12\div3}=\frac{3}{4}\)
• \(\frac{75}{100}=\frac{75\div25}{100\div25}=\frac{3}{4}\)
• \(\frac{12}{16}=\frac{12\div4}{16\div4}=\frac{3}{4}\)

Step2: Long - division

For \(2653\div25\):

• \(25\times100 = 2500\), \(2653-2500=153\)
• \(25\times6 = 150\), \(153 - 150=3\)

So \(2653\div25 = 106\frac{3}{25}\)

Step3: Multiplication with powers of 10

• \(42\times10=420\)
• \(42\times10^{2}=42\times100 = 4200\)
• \(42\times10^{3}=42\times1000 = 42000\)
• \(42\times10^{4}=42\times10000 = 420000\)

Step4: Cookies left

Since 1 dozen \( = 12\) cookies, 25 dozen \(=25\times12 = 300\) cookies.
Cookies left \(=300 - 48=252\)

Step5: Order fractions

• First set: \(\frac{1}{12}\approx0.083\), \(\frac{1}{8}=0.125\), \(\frac{5}{8}=0.625\), \(\frac{6}{8}=0.75\), \(\frac{9}{8}=1.125\), \(\frac{8}{4}=2\)

Order: \(\frac{1}{12},\frac{1}{8},\frac{5}{8},\frac{6}{8},\frac{9}{8},\frac{8}{4}\)

• Second set: \(\frac{1}{3}\approx0.333\), \(\frac{1}{2}=0.5\), \(\frac{4}{6}=\frac{2}{3}\approx0.667\), \(\frac{5}{6}\approx0.833\), \(\frac{6}{6}=1\), \(\frac{8}{6}=\frac{4}{3}\approx1.333\)

Order: \(\frac{1}{3},\frac{1}{2},\frac{4}{6},\frac{5}{6},\frac{6}{6},\frac{8}{6}\)

• Third set: \(\frac{1}{4}=0.25\), \(\frac{3}{8}=0.375\), \(\frac{1}{2}=0.5\), \(\frac{4}{4}=1\), \(\frac{7}{4}=1.75\), \(\frac{8}{4}=2\)

Order: \(\frac{1}{4},\frac{3}{8},\frac{1}{2},\frac{4}{4},\frac{7}{4},\frac{8}{4}\)

Answer:

1. Circled fractions: \(\frac{9}{12},\frac{75}{100},\frac{12}{16}\); Another equivalent fraction: \(\frac{15}{20}\) (for example)
2. \(106\frac{3}{25}\)
3. \(420\); \(4200\); \(42000\); \(420000\)
4. \(252\)
5. \(\frac{1}{12},\frac{1}{8},\frac{5}{8},\frac{6}{8},\frac{9}{8},\frac{8}{4}\); \(\frac{1}{3},\frac{1}{2},\frac{4}{6},\frac{5}{6},\frac{6}{6},\frac{8}{6}\); \(\frac{1}{4},\frac{3}{8},\frac{1}{2},\frac{4}{4},\frac{7}{4},\frac{8}{4}\)