Sure, let's find out what fraction of the pizza Heath and Janet ate together by adding the fractions of the pizza they each ate.
1. Heath's Portion:
Heath ate [tex]\( \frac{3}{5} \)[/tex] of the pizza.
2. Janet's Portion:
Janet ate [tex]\( \frac{3}{10} \)[/tex] of the pizza.
3. Common Denominator:
To add these fractions, we need a common denominator. The denominators are 5 and 10. The least common multiple (LCM) of 5 and 10 is 10.
4. Convert Heath's Fraction:
Convert [tex]\( \frac{3}{5} \)[/tex] to a fraction with a denominator of 10. This can be done by multiplying both the numerator and the denominator by 2:
[tex]\[
\frac{3}{5} \times \frac{2}{2} = \frac{6}{10}
\][/tex]
5. Add the Fractions:
Now add the fractions [tex]\( \frac{6}{10} \)[/tex] and [tex]\( \frac{3}{10} \)[/tex]:
[tex]\[
\frac{6}{10} + \frac{3}{10} = \frac{9}{10}
\][/tex]
6. Simplify if Necessary:
The fraction [tex]\( \frac{9}{10} \)[/tex] is already in its simplest form.
Therefore, the total fraction of the pizza that Heath and Janet ate together is [tex]\( \frac{9}{10} \)[/tex] or, in decimal form, approximately 0.8999999999999999.
