¹³/₄ or 3¹/₄ or 3.25
The Problem:
The Process:
Here are some early expressions that need attention.
Let us write an expression to match for 3 times as much as the sum of [tex]\frac{3}{4}[/tex] and [tex]\frac{2}{6}[/tex]
[tex]\boxed{\boxed{ \ 3 \times \bigg(\frac{3}{4} + \frac{2}{6} \bigg) \ }}[/tex]
Let us calculate the operation in parentheses at first.
[tex]\frac{3}{4} + \frac{2}{6}[/tex]
A least common multiple of 4 and 6 is 12. We use to equate the denominator.
[tex]\frac{3 \times 3}{4 \times 3} + \frac{2 \times 2}{6 \times 2}[/tex]
[tex]\frac{9}{12} + \frac{4}{12}[/tex]
[tex]\frac{13}{12}[/tex]
And now we solve the full expression.
[tex]\boxed{ \ = 3 \times \bigg(\frac{3}{4} + \frac{2}{6} \bigg) \ }[/tex]
[tex]\boxed{ \ = 3 \times \frac{13}{12} \ }[/tex]
We cross out 3 and 12 because they both can be divided.
[tex]\boxed{ \ = 1 \times 1\frac{13}{4} \ }[/tex]
[tex]\boxed{\boxed{ \ = \frac{13}{4} \ }}[/tex]
In mixed fraction:
[tex]\boxed{ \ \frac{13}{4} = \ ? \ }[/tex]
[tex]\boxed{ \ = \frac{12}{4} + \frac{1}{4} \ }[/tex]
[tex]\boxed{ \ = 3 + \frac{1}{4} \ }[/tex]
[tex]\boxed{\boxed{ \ = 3\frac{1}{4} \ }}[/tex]
In decimal:
[tex]\boxed{ \ 3\frac{1}{4} = \ ? \ }[/tex]
[tex]\boxed{ \ = 3\frac{1 \times 25}{4 \times 25} \ }[/tex]
[tex]\boxed{ \ = 3\frac{25}{100} \ }[/tex]
[tex]\boxed{\boxed{ \ = 3.25 \ }}[/tex]
[tex]\boxed{\boxed{ \ Thus, \ the \ result \ is \ \frac{13}{4} \ or \ 3\frac{1}{4} \ or \ 3.25 \ }}[/tex]
- - - - - - - - - -
Quick Steps:
Simplify [tex]\boxed{\frac{2}{6} = \frac{1}{3}}[/tex]
[tex]\boxed{ \ = 3 \times \bigg(\frac{3}{4} + \frac{2}{6} \bigg) \ }[/tex]
[tex]\boxed{ \ = 3 \times \bigg(\frac{3}{4} + \frac{1}{3} \bigg) \ }[/tex]
[tex]\boxed{ \ = 3 \times \bigg(\frac{3 \times 3}{4 \times 3} + \frac{1 \times 4}{3 \times 4} \bigg) \ }[/tex]
[tex]\boxed{ \ = 3 \times \bigg(\frac{9}{12} + \frac{4}{12} \bigg) \ }[/tex]
[tex]\boxed{ \ = 3 \times \frac{13}{12} \ }[/tex]
[tex]\boxed{\boxed{ \ = \frac{13}{4} \ }}[/tex]
[tex]\boxed{\boxed{ \ = 3\frac{1}{4} \ }}[/tex]
[tex]\boxed{\boxed{ \ = 3.25 \ }}[/tex]
Keywords: 3 times, as much as, the sum of 3/4 and 2/6, write an expression to match, and then solve, the result, in mixed fraction, decimal, ¹³/₄ or 3¹/₄ or 3.25
