Question

nit 2 test - two.

1. 2 2/3 + 1 1/2

3/5 + 2/3
4 1/3 + 2 1/2
2/3 - 1/6

1. model (draw)

3/5 × 2/3

1. model (draw)

4/6 ÷ 3/4

1. sum of 0.7 + 0.64
2. difference of 0.94 - 0.6
3. the product of 5.32 × 4.3
4. the quotient of 45.7 ÷ 1.83
5. the mean, median, mode: 4, 6, 7, 6, 9, 3, 5, 2 and range

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case 1: hours spent studying
case 2: favorite ice - cream flavors
case 3: be the analyst! dot plot: number of books read in a month

Explanation:

Step1: Solve fraction addition 1

For $\frac{3}{5}+\frac{2}{3}$, find a common - denominator. The common denominator of 5 and 3 is 15.
$\frac{3}{5}+\frac{2}{3}=\frac{3\times3}{5\times3}+\frac{2\times5}{3\times5}=\frac{9}{15}+\frac{10}{15}=\frac{9 + 10}{15}=\frac{19}{15}=1\frac{4}{15}$

Step2: Solve fraction addition 2

For $4\frac{1}{3}+2\frac{1}{2}$, convert mixed - numbers to improper fractions. $4\frac{1}{3}=\frac{4\times3 + 1}{3}=\frac{13}{3}$ and $2\frac{1}{2}=\frac{2\times2+1}{2}=\frac{5}{2}$. The common denominator of 3 and 2 is 6.
$\frac{13}{3}+\frac{5}{2}=\frac{13\times2}{3\times2}+\frac{5\times3}{2\times3}=\frac{26}{6}+\frac{15}{6}=\frac{26 + 15}{6}=\frac{41}{6}=6\frac{5}{6}$

Step3: Solve fraction subtraction

For $\frac{2}{3}-\frac{1}{6}$, the common denominator of 3 and 6 is 6.
$\frac{2}{3}-\frac{1}{6}=\frac{2\times2}{3\times2}-\frac{1}{6}=\frac{4}{6}-\frac{1}{6}=\frac{4 - 1}{6}=\frac{3}{6}=\frac{1}{2}$

Step4: Solve fraction multiplication

For $\frac{3}{5}\times\frac{2}{3}$, multiply the numerators and denominators directly.
$\frac{3}{5}\times\frac{2}{3}=\frac{3\times2}{5\times3}=\frac{6}{15}=\frac{2}{5}$

Step5: Solve fraction division

For $\frac{4}{6}\div\frac{3}{4}$, change division to multiplication by taking the reciprocal of the second fraction.
$\frac{4}{6}\div\frac{3}{4}=\frac{4}{6}\times\frac{4}{3}=\frac{4\times4}{6\times3}=\frac{16}{18}=\frac{8}{9}$

Step6: Solve decimal addition

For $0.7 + 0.64$, align the decimal points and add.
$0.7+0.64 = 1.34$

Step7: Solve decimal subtraction

For $0.94−0.6$, align the decimal points and subtract.
$0.94−0.6=0.34$

Step8: Solve decimal multiplication

For $5.32\times4.3$, multiply as if they were whole numbers and then place the decimal point.
$532\times43 = 22876$. There are $2 + 1=3$ decimal places in the factors, so $5.32\times4.3 = 22.876$

Step9: Solve decimal division

For $45.7\div1.83$, move the decimal points of both numbers to make the divisor a whole number. $45.7\div1.83=\frac{4570}{183}\approx24.97$

Step10: Find mean, median, mode and range

For the data set $4,6,7,6,9,3,5,2$:

• Mean: First, find the sum $4 + 6+7+6+9+3+5+2=42$. There are 8 data points, so the mean is $\frac{42}{8}=5.25$.
• Median: Arrange the data in ascending order: $2,3,4,5,6,6,7,9$. The median is the average of the middle two numbers (since there are 8 numbers), $\frac{5 + 6}{2}=5.5$.
• Mode: The number that appears most frequently is 6.
• Range: Subtract the smallest number from the largest number, $9 - 2=7$.

Answer:

1. $\frac{19}{15}$ (or $1\frac{4}{15}$), $6\frac{5}{6}$, $\frac{1}{2}$
2. $\frac{2}{5}$ (drawing a model for fraction - multiplication involves dividing a rectangle into 5 equal parts, shading 3 of them for $\frac{3}{5}$, then dividing those 3 parts into 3 equal sub - parts and shading 2 of the sub - parts out of the total 15 sub - parts)
3. $\frac{8}{9}$ (drawing a model for fraction - division involves representing $\frac{4}{6}$ and then showing how many $\frac{3}{4}$ fit into it)
4. $1.34$
5. $0.34$
6. $22.876$
7. Approximately $24.97$
8. Mean: $5.25$, Median: $5.5$, Mode: $6$, Range: $7$