Question

132 ÷ 11 =
( 1\frac{9}{10} )
( - 1\frac{4}{5} )
( overline{quadquad} )
( 1\frac{8}{10} )
( - \frac{1}{2} )
( overline{quadquad} )
( \frac{1}{10} )
( 1\frac{1}{5} )
( + 1 )
( overline{quadquad} )
which fact does not belong?

1. ( 9 - 2 = )
2. ( 7 + 2 = )
3. ( 2 + 7 = )
4. ( 7 - 2 = )

( 8.08 )
( - .07 )
( overline{quadquad} )
two hundred five and six tenths

Explanation:

Step1: Solve 132 ÷ 11

$132 \div 11 = 12$

Step2: Solve 414 ÷ 6

$414 \div 6 = 69$

Step3: Solve 61 ÷ 8

$61 \div 8 = 7\frac{5}{8}$

Step4: Solve $1\frac{9}{10} - 1\frac{4}{5}$

Convert to common denominator: $1\frac{9}{10} - 1\frac{8}{10} = \frac{1}{10}$

Step5: Solve $1\frac{8}{10} - \frac{1}{2}$

Convert to common denominator: $1\frac{8}{10} - \frac{5}{10} = 1\frac{3}{10}$

Step6: Solve $\frac{1}{10} + 1\frac{1}{5} + 1$

Convert to common denominator: $\frac{1}{10} + 1\frac{2}{10} + 1 = 2\frac{3}{10}$

Step7: Identify non-matching fact

Calculate each:

1. $9-2=7$
2. $7+2=9$
3. $2+7=9$
4. $7-2=5$

Facts 2 and 3 have the same sum; facts 1 and 4 have different results, but 1. $9-2=7$ and 4. $7-2=5$ are the only subtraction facts, while 2 and 3 are addition facts with the same addends. The outlier is either 1 or 4, but the only fact that does not relate to the sum of 7 and 2 is 1. $9-2=7$ (since 2 and 3 are commutative addition, 4 is subtraction of 7-2, while 1 uses 9 instead of 7 as the minuend)

Step8: Solve 8.08 - 0.07

$8.08 - 0.07 = 8.01$

Step9: Write number in digits

two hundred five and six tenths = $205.6$

Answer:

A section:
$132 \div 11 = 12$
$414 \div 6 = 69$
$61 \div 8 = 7\frac{5}{8}$

B section:
$1\frac{9}{10} - 1\frac{4}{5} = \frac{1}{10}$
$1\frac{8}{10} - \frac{1}{2} = 1\frac{3}{10}$
$\frac{1}{10} + 1\frac{1}{5} + 1 = 2\frac{3}{10}$

C section:

1. $9-2=7$
2. $7+2=9$
3. $2+7=9$
4. $7-2=5$

The fact that does not belong: 1. $9 - 2 = 7$
$8.08 - 0.07 = 8.01$
two hundred five and six tenths = $205.6$