Examples with solutions for Special Cases (0 and 1, Inverse, Fraction Line): Using fractions

Exercise #1

2016102=? 20-\frac{16-10}{2}=\text{?}

Video Solution

Step-by-Step Solution

According to the order of operations, we will first solve the fraction exercise:

16102=62=3 \frac{16-10}{2}=\frac{6}{2}=3

203=17 20-3=17

Answer

17 17

Exercise #2

25+459=? 25+\frac{45}{9}=\text{?}

Video Solution

Step-by-Step Solution

According to the order of operations, first we'll solve the fraction:

459=5 \frac{45}{9}=5

25+5=30 25+5=30

Answer

30 30

Exercise #3

1126=? \frac{1\frac{1}{2}}{6}=\text{?}

Video Solution

Step-by-Step Solution

Let's first look at the numerator of the fraction. We will convert it to an addition exercise containing two fractions:

1+12 1+\frac{1}{2}

1=22 1=\frac{2}{2}

This leaves us with:

22+126= \frac{\frac{2}{2}+\frac{1}{2}}{6}=

2+126= \frac{\frac{2+1}{2}}{6}=

3261= \frac{\frac{3}{2}}{\frac{6}{1}}=

Let's now multiply the two fractions togethernumerator by numerator and denominator by denominator:

1×32×6= \frac{1\times3}{2\times6}=

312=33×4 \frac{3}{12}=\frac{3}{3\times4}

Finally, simplify:

33×4=14 \frac{3}{3\times4}=\frac{1}{4}

14=0.25 \frac{1}{4}=0.25

Answer

0.25 0.25

Exercise #4

202+3+6=? \frac{20}{2+3}+6=\text{?}

Video Solution

Step-by-Step Solution

According to the order of operations, we will first solve the fraction exercise:

203+2=205=4 \frac{20}{3+2}=\frac{20}{5}=4

4+6=10 4+6=10

Answer

10 10

Exercise #5

3434=? \frac{\frac{3}{4}}{\frac{3}{4}}=\text{?}

Video Solution

Step-by-Step Solution

We will use the formula:

aa=1 \frac{a}{a}=1

Therefore the answer is 1

Answer

1 1