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3"},"content":{"rendered":""},"excerpt":{"rendered":""},"featured_media":0,"featured_media_url":"$undefined","acf":{"duree_estimee":10,"niveau_difficulte":"Advanced","categorie":"Fractions & Rational Expressions","nombre_questions":9,"score_minimum":80,"ordre_questions":"Fixe","questions":[{"id":"cmme85dms0037ju04lum9ajgz","texte_question":"

Simplify the expression:

$$\\frac{\\frac{2}{5} + \\frac{1}{3}}{\\frac{3}{4} - \\frac{1}{2}} \\div \\frac{5}{6}$$

","type_question":"QCM","explication":"

Step 1: Simplify the numerator

$$\\frac{2}{5} + \\frac{1}{3} = \\frac{6}{15} + \\frac{5}{15} = \\frac{11}{15}$$

Step 2: Simplify the denominator

$$\\frac{3}{4} - \\frac{1}{2} = \\frac{3}{4} - \\frac{2}{4} = \\frac{1}{4}$$

Step 3: Divide the numerator by the denominator

$$\\frac{11}{15} \\div \\frac{1}{4} = \\frac{11}{15} \\times \\frac{4}{1} = \\frac{44}{15}$$

Step 4: Divide by $$\\frac{5}{6}$$

$$\\frac{44}{15} \\div \\frac{5}{6} = \\frac{44}{15} \\times \\frac{6}{5} = \\frac{264}{75}$$

Step 5: Simplify the final result

$$\\frac{264}{75} = \\frac{88}{25}$$

Final Answer: $$\\frac{88}{25}$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

$$\\frac{44}{15}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{88}{35}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{88}{25}$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{22}{9}$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmme85dms003cju04l3eoi3cl","texte_question":"

Simplify the expression:

$$\\frac{\\left( \\frac{1}{x} - \\frac{1}{y} \\right)}{\\left( \\frac{1}{x} + \\frac{1}{y} \\right)}$$

","type_question":"QCM","explication":"

Step 1: Simplify the numerator

$$\\frac{1}{x} - \\frac{1}{y} = \\frac{y - x}{xy}$$

Step 2: Simplify the denominator

$$\\frac{1}{x} + \\frac{1}{y} = \\frac{y + x}{xy}$$

Step 3: Divide the simplified numerator by the simplified denominator

$$\\frac{\\frac{y - x}{xy}}{\\frac{y + x}{xy}} = \\frac{y - x}{xy} \\cdot \\frac{xy}{y + x}$$

Step 4: Cancel common terms

$$\\frac{y - x}{y + x}$$

Final Answer: $$\\frac{y - x}{y + x}$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$\\frac{2y + x}{y + x}$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$\\frac{y - x}{y + x}$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{y - x}{y}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{- x}{y + x}$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmme85dms003hju04461dlfue","texte_question":"

Simplify the expression:

$$\\frac{\\frac{7}{4} - \\frac{2}{3}}{\\frac{7}{4} - \\frac{2}{3} - \\frac{1}{2}} \\div \\left( \\frac{7}{4} - \\frac{2}{3} - \\frac{1}{2} \\right)$$

","type_question":"QCM","explication":"

Step 1: Simplify the numerator

$$\\frac{7}{4} - \\frac{2}{3} = \\frac{21}{12} - \\frac{8}{12} = \\frac{13}{12}$$

Step 2: Simplify the denominator

$$\\frac{7}{4} - \\frac{2}{3} - \\frac{1}{2} = \\frac{21}{12} - \\frac{8}{12} - \\frac{6}{12} = \\frac{7}{12}$$

Step 3: Divide the simplified numerator by the simplified denominator

$$\\frac{\\frac{13}{12}}{\\frac{7}{12}} = \\frac{13}{12} \\cdot \\frac{12}{7} = \\frac{13}{7}$$

Step 4: Divide by the remaining term

$$\\frac{13}{7} \\div \\frac{7}{12} = \\frac{13}{7} \\cdot \\frac{12}{7} = \\frac{156}{49}$$

Final Answer: $$\\frac{156}{49}$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

$$\\frac{56}{49}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$\\frac{156}{49}$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"$$$\\frac{21}{13}$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{49}{52}$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmme85dms003mju04p3bbs1ba","texte_question":"

A cake is divided into 10 portions. Each portion is then cut into half, creating two equal slices per portion. If Mia eats 5 of these slices, what fraction of the whole cake does she eat?

","type_question":"QCM","explication":"

Step 1: Total number of slices

The cake is divided into 10 portions.

Each portion is further divided into 2 slices.

Thus, the total number of slices is:

$$10 \\times 2 = 20$$

Step 2: Number of slices Mia eats

Mia eats 5 slices.

Step 3: Fraction of the cake eaten

The fraction of the whole cake Mia eats is:

$$\\frac{5}{20}$$

Step 4: Simplify the fraction

$$\\frac{5}{20} = \\frac{1}{4}$$

Final Answer: $$\\frac{1}{4}$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

$$\\frac{1}{8}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$\\frac{1}{2}$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{1}{4}$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{1}{10}$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmme85dmt003rju044jhpf5wp","texte_question":"

Emily used a coupon to buy a jacket for $$C$$ dollars less than the retail price of $$P$$. The discounted price that Emily paid represents what fraction of the retail price of the jacket?

","type_question":"QCM","explication":"

Step 1: Determine the discounted price Emily paid.

The retail price is $$P$$, and the discount is $$C$$. Therefore, the discounted price is:

$$P - C.$$

Step 2: Express the fraction of the retail price.

The fraction of the retail price is the discounted price divided by the retail price: $$\\frac{P - C}{P}.$$

Final Answer: $$\\frac{P - C}{P}$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$\\frac{C}{P}$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$\\frac{P}{C}$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$\\frac{P-C}{C}$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{P-C}{P}$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmme85dmt003wju04c6o8e0cz","texte_question":"

If a mixed fraction is denoted by $$X\\frac{3}{4}=\\frac{9}{4}$$, then what is the value of: $$\\frac{1}{3X-4}$$?

","type_question":"QCM","explication":"

Step 1: Convert the mixed fraction to an improper fraction

A mixed number is written as:

$$X\\frac{3}{4} = X + \\frac{3}{4}$$

Given:

$$X + \\frac{3}{4} = \\frac{9}{4}$$

Step 2: Solve for $$X$$

Subtract $$\\frac{3}{4}$$ from both sides:

$$X = \\frac{9}{4} - \\frac{3}{4} = \\frac{6}{4} = \\frac{3}{2}$$

Step 3: Evaluate the expression $$\\frac{1}{3X - 4}$$

Substitute $$X = \\frac{3}{2}$$:

$$3X = 3 \\cdot \\frac{3}{2} = \\frac{9}{2}$$

$$3X - 4 = \\frac{9}{2} - \\frac{8}{2} = \\frac{1}{2}$$

Now take the reciprocal:

$$\\frac{1}{3X - 4} = \\frac{1}{\\frac{1}{2}} = 2$$

Final Answer: $$2$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

$$\\frac{3}{4}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$2$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"$$$\\frac{1}{4}$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{1}{3}$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmme85dmt0041ju04wz6ip1hg","texte_question":"

What is the value of $$(m - 3)^3$$ if $$m = \\left(\\frac{5}{3} + \\frac{5}{6} + \\frac{1}{2}\\right)$$?

","type_question":"QCM","explication":"

First, compute the value of $$m$$:

Find a common denominator for the fractions:

$$\\frac{5}{3} = \\frac{10}{6}, \\quad \\frac{1}{2} = \\frac{3}{6}$$

So,

$$m = \\frac{10}{6} + \\frac{5}{6} + \\frac{3}{6} = \\frac{18}{6} = 3$$

Now substitute into the expression:

$$(m - 3)^3 = (3 - 3)^3 = 0^3 = 0$$

Final answer: $$0$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

$$\\frac{100}{7}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$\\frac{27}{6}$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$\\frac{1000}{27}$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$0$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmme85dmt0046ju04xsxtvxr5","texte_question":"

If $$N = \\frac{S}{\\frac{p}{q} - 1}$$, then express $$q$$ in terms of $$N, S, p$$.

","type_question":"QCM","explication":"

Start by rewriting the equation:

$$N = \\frac{S}{\\frac{p}{q} - 1}$$

Multiply both sides by $$\\left(\\frac{p}{q} - 1\\right)$$:

$$N\\left(\\frac{p}{q} - 1\\right) = S$$

Distribute $$N$$:

$$\\frac{Np}{q} - N = S$$

Add $$N$$ to both sides:

$$\\frac{Np}{q} = S + N$$

Multiply both sides by $$q$$:

$$Np = q(S + N)$$

Now divide both sides by $$(S + N)$$:

$$q = \\frac{Np}{S + N}$$

Final Answer: $$q = \\frac{Np}{S + N}$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

$$\\frac{NS}{p + N}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{Np}{S + N}$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{NS}{p + s}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{pS}{2N}$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmme85dmt004bju04xakensxx","texte_question":"

If $$p = \\frac{1 + \\frac{x}{y}}{1 + \\frac{xy}{z^2}}$$, $$x = \\frac{z}{2}$$ and $$y = 3z$$, find the value of $$p$$.

","type_question":"QCM","explication":"

Substitute $$x = \\frac{z}{2}$$ and $$y = 3z$$ into the expression for $$p$$:

First, compute $$\\frac{x}{y}$$:

$$\\frac{x}{y} = \\frac{\\frac{z}{2}}{3z} = \\frac{1}{6}$$

Now compute $$\\frac{xy}{z^2}$$:

$$\\frac{xy}{z^2} = \\frac{\\left(\\frac{z}{2}\\right)(3z)}{z^2} = \\frac{3z^2}{2z^2} = \\frac{3}{2}$$

Now plug into the original expression:

$$p = \\frac{1 + \\frac{1}{6}}{1 + \\frac{3}{2}} = \\frac{\\frac{7}{6}}{\\frac{5}{2}} = \\frac{7}{6} \\cdot \\frac{2}{5} = \\frac{14}{30} = \\frac{7}{15}$$

Final answer: $$p = \\frac{7}{15}$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$\\frac{3}{2}$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$\\frac{3}{5}$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{7}{6}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{7}{15}$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]}]},"categories":["fractions-&-rational-expressions"],"date":"2026-02-15T03:16:11.879Z","modified":"2026-03-06T01:37:15.844Z"}}]]}]}]]