Question

nit 2 test - tues.

1. @2 3/5 + 1 2/5 = 3 4/5

@. 3/5 + 2/3 = 1 4/15
@ 4 3/7 + 2 1/2 = 6 13/14
@ 2/3 - 1/5 = 7/15

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, and range

Explanation:

Step1: Add mixed - numbers

For \(2\frac{2}{3}+1\frac{2}{3}\), first add the whole - numbers \(2 + 1=3\), then add the fractions \(\frac{2}{3}+\frac{2}{3}=\frac{4}{3}=1\frac{1}{3}\), and \(3 + 1\frac{1}{3}=4\frac{1}{3}\) (the original answer \(3\frac{4}{5}\) is incorrect).

Step2: Add fractions

For \(\frac{3}{5}+\frac{2}{3}\), find a common denominator. The common denominator of 5 and 3 is 15. So \(\frac{3}{5}+\frac{2}{3}=\frac{3\times3}{5\times3}+\frac{2\times5}{3\times5}=\frac{9}{15}+\frac{10}{15}=\frac{19}{15}=1\frac{4}{15}\) (the original answer \(1\frac{1}{15}\) is incorrect).

Step3: Add mixed - numbers

For \(4\frac{3}{7}+2\frac{1}{2}\), first convert to improper fractions. \(4\frac{3}{7}=\frac{4\times7 + 3}{7}=\frac{31}{7}\) and \(2\frac{1}{2}=\frac{2\times2+1}{2}=\frac{5}{2}\). The common denominator of 7 and 2 is 14. \(\frac{31}{7}+\frac{5}{2}=\frac{31\times2}{7\times2}+\frac{5\times7}{2\times7}=\frac{62}{14}+\frac{35}{14}=\frac{97}{14}=6\frac{13}{14}\) (correct).

Step4: Subtract fractions

For \(\frac{2}{3}-\frac{1}{5}\), the common denominator is 15. \(\frac{2}{3}-\frac{1}{5}=\frac{2\times5}{3\times5}-\frac{1\times3}{5\times3}=\frac{10}{15}-\frac{3}{15}=\frac{7}{15}\) (correct).

Step5: Multiply fractions

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

Step6: Divide fractions

For \(\frac{4}{6}\div\frac{3}{4}\), multiply by the reciprocal of the second fraction. \(\frac{4}{6}\times\frac{4}{3}=\frac{16}{18}=\frac{8}{9}\).

Step7: Add decimals

For \(0.7 + 0.64\), line up the decimal points: \(0.70+0.64 = 1.34\).

Step8: Subtract decimals

For \(0.94−0.6\), line up the decimal points: \(0.94 - 0.60=0.34\).

Step9: Multiply decimals

For \(5.32\times4.3\), \(532\times43 = 22876\). There are \(2 + 1=3\) decimal places in the factors, so the product is \(22.876\).

Step10: Divide decimals

For \(45.7\div1.83\), move the decimal points of both numbers to make the divisor a whole number. \(4570\div183\approx24.97\).

Step11: Find mean, median, mode, and range

For the data set \(4,6,7,6,9,3,5\):

• Mean: \(\frac{4 + 6+7+6+9+3+5}{7}=\frac{40}{7}\approx5.71\).
• First, order the data set: \(3,4,5,6,6,7,9\). Median is the middle number, which is 6.
• Mode is the number that appears most frequently, which is 6.
• Range: \(9 - 3=6\).

Answer:

1. \(4\frac{1}{3}\)
2. \(\frac{2}{5}\)
3. \(\frac{8}{9}\)
4. \(1.34\)
5. \(0.34\)
6. \(22.876\)
7. Approximately \(24.97\)
8. Mean: \(\frac{40}{7}\approx5.71\), Median: 6, Mode: 6, Range: 6