Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify.
12(1)/(2)-4(7)/(10)= _____

Simplify.\newline12124710=_____ 12 \frac{1}{2}-4 \frac{7}{10}= \_\_\_\_\_

Full solution

Q. Simplify.\newline12124710=_____ 12 \frac{1}{2}-4 \frac{7}{10}= \_\_\_\_\_
  1. Convert to Improper Fractions: Convert mixed numbers to improper fractions.\newline12(12)12\left(\frac{1}{2}\right) can be converted to an improper fraction by multiplying the whole number 1212 by the denominator 22 and adding the numerator 11, then placing the result over the original denominator.\newline12(12)=(12×2+1)/2=(24+1)/2=25/2.12\left(\frac{1}{2}\right) = \left(12 \times 2 + 1\right)/2 = \left(24 + 1\right)/2 = 25/2.\newlineSimilarly, 4(710)4\left(\frac{7}{10}\right) can be converted to an improper fraction by multiplying the whole number 44 by the denominator 1010 and adding the numerator 77, then placing the result over the original denominator.\newline4(710)=(4×10+7)/10=(40+7)/10=47/10.4\left(\frac{7}{10}\right) = \left(4 \times 10 + 7\right)/10 = \left(40 + 7\right)/10 = 47/10.
  2. Subtract Fractions: Subtract the two improper fractions.\newlineTo subtract fractions, they must have a common denominator. The least common denominator (LCD) for 22 and 1010 is 1010. We need to convert 252\frac{25}{2} to a fraction with a denominator of 1010.\newline252=(25×52×5)=12510\frac{25}{2} = \left(\frac{25 \times 5}{2 \times 5}\right) = \frac{125}{10}.\newlineNow we can subtract 4710\frac{47}{10} from 12510\frac{125}{10}.\newline125104710=(1254710)=7810\frac{125}{10} - \frac{47}{10} = \left(\frac{125 - 47}{10}\right) = \frac{78}{10}.
  3. Simplify Resulting Fraction: Simplify the resulting fraction. 7810\frac{78}{10} can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 22. 7810=(78/2)(10/2)=395\frac{78}{10} = \frac{(78/2)}{(10/2)} = \frac{39}{5}.
  4. Convert Back to Mixed Number: Convert the improper fraction back to a mixed number if necessary.\newlineSince 395\frac{39}{5} is an improper fraction, we can convert it back to a mixed number. 3939 divided by 55 is 77 with a remainder of 44.\newline395=7(45)\frac{39}{5} = 7\left(\frac{4}{5}\right).